A257024 Number of squares in the quarter-sum representation of n.

1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 2, 3, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 2, 2

Offset

0,6

Comments

Every positive integer is a sum of at most four distinct quarter squares; see A257019.

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Example

Quarter-square representations:
r(5) = 4 + 1, so a(5) = 2;
r(11) = 9 + 2, so a(11) = 1;
r(35) = 30 + 4 + 1, so a(35) = 2.

Mathematica

z = 100; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];
s[n_] := Table[b[n], {k, b[n + 1] - b[n]}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; Take[g, 100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]
sq = Table[n^2, {n, 0, 1000}]; t = Table[r[n], {n, 0, z}]
u = Table[Length[Intersection[r[n], sq]], {n, 0, 250}]

Crossrefs

Cf. A002620, A257019, A257020, A257021, A257022.

Sequence in context: A054528 A025884 A352427 * A334996 A124433 A371074

Adjacent sequences: A257021 A257022 A257023 * A257025 A257026 A257027

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2015

Status

approved